Never stop or never start? Optimal stopping under a mixture of CPT and EUT preferences

Xuedong He and Sang Hu

Journal of Economic Theory, 2024, vol. 222, issue C

Abstract: We consider the problem of finding the best time to stop a diffusion process for an agent with a preference model that is a mixture of expected utility theory (EUT) and cumulative prospect theory (CPT). In view of time-inconsistency, we consider two types of agents: a naive agent, who is not aware of the time-inconsistency and thus re-plans at every instant, and a sophisticated agent, who is aware of the time-inconsistency and takes a so-called intra-personal equilibrium strategy by correctly anticipating her actions in the future. We show that under a wide range of the CPT preference parameter values, the naive agent will never stop. For a sophisticated agent, we use a different notion of intra-personal equilibrium from the one employed by Ebert and Strack (2018). We show that any two-threshold strategy, which is to stop when the diffusion process reaches either an upper threshold or a lower threshold, cannot be an intra-personal equilibrium if the agent overweights worst, unlikely outcomes disproportionally. We derive a sufficient and necessary condition for the strategy of stopping everywhere to be an intra-personal equilibrium and show that this condition does not hold and thus the sophisticated agent may choose to start the diffusion process for some commonly used probability weighting functions.

Keywords: Cumulative prospect theory; Optimal stopping; Naive agents; Sophisticated agents; Intra-personal equilibrium (search for similar items in EconPapers)
JEL-codes: D81 D90 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:222:y:2024:i:c:s0022053124001315

DOI: 10.1016/j.jet.2024.105925

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